Euclidean Distance

$\Vert \vec{x}{\Vert }_2=\sqrt{\sum _i{x}_i^2}$

• Interestingly, for a given set of points ${\vec{x}}_i$, the points that minimizes the sum of euclidean distances to ${\vec{x}}_i$ is their mean

$d=\sqrt{(x_i^{\prime }-x_i{)}^2}$

• Distance between two points
• Assuming Einstein notation
• $x_i$ refers to summing over all coordinate differences